**Tasks to do: **

- Properties of 2nd order systems, inverse Z-transform of higher-order systems.
- For discrete-time systems described by following difference
equations draw block scheme, compute difference equation, transfer
function, zeros and poles of transfer function, impulse
response, and estimate frequency response.
- y[n] = x[n] + 2 x[n-1] + 1.5 y[n-1] - y[n-2]
- y[n] = 0.4455 x[n-1] + 1.2728 y[n-1] - 0.81 y[n-2]
- y[n] = x[n] + 0.81 x[n-2]
- Observe the change of the frequency response and zero-poles locations
for the following systems:
- y[n] = x[n] + 0.81 x[n-2]
- y[n] = x[n] + 0.64 x[n-2]
- y[n] = x[n] + 0.925 x[n-2]
- y[n] = x[n] - 0.81 y[n-2]
- y[n] = x[n] - 0.64 y[n-2]
- y[n] = x[n] - 0.925 y[n-2]

- Only in MATLAB: "all=pole" filter with the pair of complex conjugate poles p_1 = 0.9 *exp ( +/- j * pi/4 )
- y[n] = x[n] + x[n-1] + x[n-2] + ... + x[n-9] ;
- y[n] = x[n] - x[n-6]
- y[n] = x[n] - x[n-9]

- For above described system observe in MATLAB:
- zeros and poles of transfer function (fnc
*zplane*,*roots*) - frequency response of the system (fnc
*freqz*) - impulse response of given system (fnc
*impz*) - check also interactive tool
*fvtool*

Perform the

**filtering of white noise**using the**system No. 4**. The noise should have uniform distribution and the length of 10000 samples. Display:**1st checked result (1 point):**- time waveforms of input and output signals,
- spectrograms of input and output signals computed with the length of short-time frame of 256 samples,
- frequency response of used filter,
**2nd checked result (1 point):**- short-time power spectra of input and output signals computed from the short-time frame with the length of 256 samples,
- twoside smoothed estimation of PSD for input and output signals, the short-time frame should have the length of 256 samples,

- zeros and poles of transfer function (fnc